Inventions represent specific technologies or practices that can be adopted by the state in order to get a specific military, economic, or political effects and bonuses. Every invention is associated with a specific field of advances and is structured as part of a tree, with most inventions requiring prerequisites that must be adopted first before the next invention can be taken.
Some inventions also have additional requirements, such as requiring a 
primary or integrated culture of a specific culture group, a certain 
government type, a certain country rank, particular DLCs, or simply only being available to certain countries. These culture, government, tag, rank, and DLC-specific inventions generally will not appear unless their requirements are met.
Most inventions have modifiers that are applied when active, which are permanent modifiers that the country gains once it adopts the invention. Some inventions also have when activated effects, with some merely descriptions of buildings, 
wonder effects, 
subject types, or other mechanics that are permanently unlocked once the invention is adopted, while others are one-time effects and bonuses that triggered immediately when the invention is purchased. Some inventions are keystone inventions that are specially marked with a more elaborate border; these mark inventions that are considered important, whether because they have a strong effect or modifier or unlock particularly important mechanics, but are not mechanically different in any way from normal inventions.
Unlike advances, no country has any inventions adopted at the start. However, most countries that start with a higher level of advances do start with a corresponding number of innovations to purchase inventions with at the beginning of the game.
Innovations
Each invention requires spending one innovation to adopt. Innovations are gained primarily from technological advances, which grant one innovation for each level, and can also be gained by adopting certain 
military traditions, as a reward for certain specific 
missions, as a rare outcome of successfully stealing technology, or occasionally from 
researchers that have the 
obsessive, 
intelligent, 
polymath, or 
scholar traits. All innovations are equal, and there is no requirement to use innovations gained from a particular field of advances on an invention inside that field. It is entirely possible to invest all of a country's innovations on a single field of inventions, if the country is willing to neglect the others. Note that there are many more inventions than it is realistically possible to adopt over the course of the game, and even technologically advanced countries will be forced to pick and choose which areas they want to prioritize and which inventions they will leave for later - or not at all.
